Calendar: 1882-1883 Page 631

62S GENERAL LITERATURE AND SCIENCE 14 Prove that the differential equation of central orbit is de נ ψφ particle is projected at distance with velocity equal to the velocity in circle at the same distance and at an angle with the distance the force being Μ μ μ determine the orbit and shew that the time to the centre of force is ζ 7Γ Divisions II eonutn If two straight lines cut one another the vertical or opposite angles shall be equal same and vertical angle If side of any triangle be produced the exterior angle is equal to the two interior and opposite angles and the three interior angles of every triangle are together equal to two right angles All the interior angles of any rectilineal figure together with four right angles are equal to twice as many right angles as the figure has sides Compare the magnitudes of an angle of regular hexagon and octagon If straight line be divided into two equal and also into two unequal parts the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section the one another